Steven Gerrard admits a "culture of fear" hinders England's chances of success - but he believes the right man in charge can lead to a quick change in the national team's fortunes.
England's Euro 2016 campaign came to an embarrassing end on Monday, as they lost 2-1 to Iceland in the last-16 tie in Nice.
Gerrard - who captained England during their disastrous 2014 World Cup campaign that saw Hodgson's squad fail to get beyond the group stages - feels the "hysteria" around England takes a toll on the players.
He also pinpointed the weight of history as another factor to explain such disappointing results - England have not won a major international tournament since the 1966 World Cup.
"We are not a side or nation with a culture of winning at the European Championship and the World Cup and the psychological impact of that is there to see at the first hint of trouble," Gerrard wrote in his column in The Daily Telegraph.
"There is no environment of calm around the national team. There never has been. It is always hysteria. There is a culture of fear within and it has not been addressed.
"It is all very well for the media to shake their heads at that and say we should be stronger and more level-headed in those situations but there is a weight of history to contend with.
"It has become a massive burden. When calm heads were needed out there, everyone was looking at each other hoping someone was going to pull something out the bag for us. Very few were capable of taking on the responsibility."
The defeat to Iceland proved to be Roy Hodgson's final game in charge, meaning the Football Association are now beginning the search for a new manager.
Gerrard used the examples of England's cricket and rugby teams, who are led by Australians Trevor Bayliss and Eddie Jones respectively, to show how a "shrewd appointment" can make a huge difference in a short space of time.
"Over the last 12 months the England cricket and rugby teams have faced the same crisis as we do now after miserable campaigns in international tournaments," he continued.
"The same arguments were no doubt presented, players attacked for not being good enough and many saying it is wrong to focus on individuals when it is the whole system that is to blame.
"What the likes of Trevor Bayliss and Eddie Jones have demonstrated is that if you have the right man in charge of the talent it can come together quickly.
"That is the side of the fence I am on. With a shrewd appointment, we can make more of the quality we have."